Master’s Degree Thesis IP501909 MSc Thesis, discipline ...
Transcript of Master’s Degree Thesis IP501909 MSc Thesis, discipline ...
Master of Science in Product and System Design
Submission date: 11th June 2019
Supervisor: Henry Piehl, NTNU
Co-Supervisor: Jagan Gorle, Parker Hannifin
Norwegian University of Science and Technology
Department of Ocean operations and Civil engineering
Ålesund, Norway
Master’s Degree Thesis
IP501909 MSc Thesis, discipline-oriented master
Numerical analysis of water absorption from
hydraulic oil flow using cellulose porous media
Mohammed Fazin Kareem Palikandy Meethal /10008
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Date: 11.06.2019
MASTER THESIS 2019
FOR
STUD.TECHN. Mohammed Fazin Kareem Palikandy Meethal
Numerical analysis of water absorption from hydraulic oil
flow using cellulose porous media
Background and Objective
Parker Hannifin,-a Fortune 250 Company, is a global leader in motion and control technologies
for the applications in the fields of aerospace, climate control, electromechanics, filtration, fluid
& gas handling, hydraulics, process control, and sealing and shielding. The Hydraulic and
Industrial Process Filtration Division EMEA develops manufactures and delivers the products
and solutions for fluid filtration and condition monitoring to serve the markets of marine, power
generation, and mobile hydraulic machines.
The porous medium of the mechanical filter, called filter element, is usually made up of
multiple layers of different materials for an effective filtration/separation process. The foreign
matter in the hydraulic oil causes major problems such as component wear, reduced system
efficiency and operational life.
This thesis work focuses on the liquid (water) contaminant and its separation from the oil using
a commercial filter’s media pack. The filter element contains different layers including the
cellulose-based porous medium, non-woven layers, and supporting meshes. Water is absorbed
by the cellulose layers while the oil passes through. The aim of this project is to gain insights
into water absorption and its mechanics using computations and experiments. Computational
Fluid Dynamics (CFD) models of flow through porous media are developed and validated
using the Multipass (ISO 16889) measurements. Water absorption of the chosen porous media
tests on a tailor-made test rig, and a pertinent numerical model is developed to examine the
motion of the water droplets through randomly generated fibers of porous material using
Discrete Phase Model. These CFD models can help in determining the pressure drop across the
filtering media and the phase-separation efficiency which can be used in improving the fiber
orientation, thickness, material of the media used in water absorption.
The following tasks are to be considered:
1. Literature study on water separation methods, multiphase flows, porous media, Discrete
Phase Model (DPM)
2. Experiments for pressure drop measurements and water absorption tests
3. 3D random fiber generation
4. CFD modeling for estimating the pressure drop across a porous domain, and water
absorption by microstructural porous media
The master thesis shall comprise of 30 credits. The thesis shall be written as a research report
with Introduction, literature review, methodology, conclusions, references, table of contents,
etc. To ease the evaluation of the thesis, the references of the corresponding texts, tables, and
figures are to be clearly stated. The results are to be thoroughly treated, presented in clearly
arranged tables and/or graphs and discussed in detail.
The thesis is carried out at Parker’s R&D lab in Urjala, Finland and hence the candidate as to
abide by the terms of the company and, keep in frequent contact with the academic supervisor
for the progress of his thesis work.
The report shall be submitted online in INSPERA according to the standard procedures to the
Department of Ocean operations and Civil engineering within 11th June 2019.
Supervisor: Henry Piehl, Academic Supervisor, NTNU
Mohammed Fazin Kareem Palikandy Meethal
Candidate Signature
Preface
The thesis was written as part of my Master Science degree program in Product and System
design at NTNU (Norwegian University of Science and Technology), Ålesund, Norway, during
Spring 2019 under the supervision of Dr-Ing. Henry Piehl in the Department of Ocean
operations and Civil engineering and also, under the co-supervision of Dr. Jagan Gorle,
Principal R&D Engineer at the Hydraulic and Industrial Process Filtration Division of Parker
Hannifin in Urjala, Finland
I would like to acknowledge the support, patience, and guidance of the following people
without whom, the thesis would not have been completed. Firstly, I would like to thank my
thesis supervisor Dr-Ing. Henry Piehl and my course coordinator Prof. Henrique M. Gaspar
for their support throughout the course. Their guidance has navigated me effortlessly to the
thesis completion.
I would like to express my respect and gratitude to my co-supervisor Dr. Jagan Gorle,
Principal R&D Engineer at Parker Hannifin, for giving me an opportunity to do the thesis in
their lab and sharing his ideas, information, and assistance throughout my research period. His
motivation, help, and support are the reasons for having the work on track and completing the
thesis in time.
I would also like to acknowledge, Mr. V.M Heiskanen, Ms. Satu Nissi and Mr. Martin
Majas for their useful inputs and helping me in conducting the experiments at Parker’s R&D
Lab. The lively environment and encouragement in the lab have a stress-free worktime.
Last but not least, I would like to thank my parents, siblings, and friends for their support and
continuous encouragement throughout my studies at NTNU.
Mohammed Fazin Kareem Palikandy Meethal
Ålesund, 11th June 2019
Abstract
Filtration is a part of the wider concept of contamination control. Contaminants in the hydraulic
oil can be in the form of solids, liquids, and gas. Particularly, water in oil can cause major
problems in a given hydraulic system such as corrosion and wear of components which would
not only deteriorate the efficiency of the system but also lead to extensive maintenance. The
type of material used in order to filter water out of the hydraulic oil has to be considered. A
filter media is made up of cellulose fibrous media with numerous pores. Due to its property of
affinity towards water, the majority of water molecules gets absorbed by its fibrous elements
and allowing the oil to pass through it. The filtration efficiency is a function of fluid flow,
temperature, operation, and calibration of feed systems.
In this thesis a numerical model to estimate the pressure drop over a porous domain is
developed. The model is validated using the standard multipass experiment. The CFD model
is further developed with 3D random fiber distribution in the porous zone that is used in
separating the water in hydraulic oil flows. The developed fibers are distributed over a domain
which is equivalent to the overall dimension of the filter media. Ansys fluent’s Discrete Phase
Model is used in order to study the water absorption in filter media. The resulting simulation
is validated with the water absorption test experiment. The pressure drop and efficiency of the
filter media estimated can be used for studying filters properties, type, layer consideration and
fiber orientation required for different industrial water absorption applications.
Table of Contents
ABSTRACT ......................................................................................................... 7
1 INTRODUCTION ........................................................................................ 1
1.1 BACKGROUND ............................................................................................................. 1
1.2 PARKER’S DUPLEX FILTER FOR WATER SEPARATION FROM HYDRAULIC OIL ............... 1
1.3 PROBLEM DEFINITION ................................................................................................. 2
1.3.1 Water is highly reactive..................................................................................................... 3
1.3.2 Symptoms of water contamination are explained below ................................................... 4
1.4 OBJECTIVE .................................................................................................................. 6
1.5 SCOPE ......................................................................................................................... 7
1.6 CONCLUSION ............................................................................................................... 8
2 LITERATURE REVIEW ............................................................................ 9
2.1 INTRODUCTION ........................................................................................................... 9
2.2 POROUS MEDIA ........................................................................................................... 9
2.2.1 Porosity ........................................................................................................................... 10
2.2.2 Permeability .................................................................................................................... 10
2.3 WATER SEPARATION CONCEPTS ................................................................................ 11
2.3.1 Coalescence ..................................................................................................................... 11
2.3.2 Absorption ....................................................................................................................... 12
2.4 WATER ABSORPTION THROUGH CELLULOSE MEDIA ................................................. 13
2.5 DARCY AND FORCHHEIMER LAW .............................................................................. 13
2.6 COMPUTATIONAL FLUID DYNAMICS (CFD) .............................................................. 14
2.6.1 Multiphase flow .............................................................................................................. 16
2.7 RESEARCH METHODS ................................................................................................ 18
2.7.1 Computational methods................................................................................................... 18
2.7.2 Turbulence modeling ...................................................................................................... 22
2.7.3 Fluent solver .................................................................................................................... 23
2.7.4 Experimental methods ..................................................................................................... 23
2.8 CONCLUSIONS ........................................................................................................... 25
3 METHODOLOGY ..................................................................................... 27
3.1 INTRODUCTION ......................................................................................................... 27
3.2 PRESSURE DROP TESTS USING MULTIPASS METHOD .................................................. 29
3.2.1 Test 1: Pleated element ................................................................................................... 31
3.2.2 Test 2: Flat sheet ............................................................................................................. 33
3.3 TEST BENCH FOR WATER ABSORPTION FROM HYDRAULIC FLOWS.............................. 34
3.4 COMPUTATIONAL FRAMEWORK ................................................................................ 36
3.4.1 Case 1: Model without Fibers ......................................................................................... 37
3.4.2 Case 2: Model with Fibers .............................................................................................. 43
3.5 CONCLUSION ............................................................................................................. 50
4 RESULTS AND DISCUSSIONS .............................................................. 51
4.1 PRESSURE DROP FOR FLAT SHEET AND PLEATED ELEMENT FROM MULTIPASS TEST .. 51
4.2 FLAT SHEET ANALYSIS USING CFD (CFD MODEL WITHOUT FIBERS) ........................ 52
4.3 EXPERIMENT VS NUMERICAL SIMULATION OF FLAT SHEET ....................................... 56
4.4 PRESSURE DROP FROM THE WATER ABSORPTION TEST .............................................. 56
4.5 PRESSURE DROP ESTIMATION USING CFD MODEL WITH FIBERS ................................ 57
4.6 EXPERIMENT VS NUMERICAL SIMULATION OF MODEL WITH FIBERS .......................... 59
4.7 WATER REMOVAL EFFICIENCY .................................................................................. 60
4.8 LIMITATION OF THE MODEL....................................................................................... 61
5 CONCLUSION ........................................................................................... 62
6 FUTURE WORK ....................................................................................... 63
7 REFERENCES ........................................................................................... 64
APPENDIX A: ................................................................................................... 66
APPENDIX B .................................................................................................... 68
APPENDIX C .................................................................................................... 71
List of Figures
Figure1. 1: Duplex Filter (left), and the water absorption filter element (right) ....................... 2
Figure1. 2: Water reacts chemically with the fluid and system components ............................. 4
Figure1. 3: Water changes the viscosity of an oil base fluid (Parker Corporation, 2019) ......... 5
Figure1. 4: Scope of the thesis ................................................................................................... 8
Figure 2. 1: Two droplets going to collide (Left) and Droplets forming a thin film after a
finite time (Right) .................................................................................................................... 12
Figure 2. 2: Process of water absorption by a cellulose fiber .................................................. 12
Figure 2. 3: Flow regimes in porous media (Skjetne & Auriault, 1999) ................................. 13
Figure 2. 4: Overview of the modeling approaches (Tsuji, 2008) ........................................... 16
Figure 2. 5: Droplet distribution defining an initial spatial distribution of particle streams
(Fluent, 2019) ........................................................................................................................... 20
Figure 2. 6: Reflect Boundary condition in fluent for discrete phase (Fluent, 2019) .............. 21
Figure 2. 7: Trap Boundary condition in Fluent for discrete phase (Fluent, 2019) ................. 21
Figure 2. 8: Escape Boundary condition in Fluent for discrete phase (Fluent, 2019) ............. 22
Figure 3. 1: Detailed methodology .......................................................................................... 28
Figure 3. 2: Schematic diagram of Multipass test bench ......................................................... 29
Figure 3. 3: Multipass test bench ............................................................................................. 30
Figure 3. 4: Layers in the filter element ................................................................................... 31
Figure 3. 5: Housing used for Pleated element in the test rig .................................................. 32
Figure 3. 6: Flat sheet and its layer orientation used for pressure drop test ............................ 33
Figure 3. 7: Housing used for flat sheet in the test bench ........................................................ 33
Figure 3. 8: Schematic diagram of the experimental system of water absorption test ............ 35
Figure 3. 9: Schematic of the general CFD setup. ................................................................... 36
Figure 3. 10: Pleated media stretched to the flat sheet and the size considered for CFD
modeling .................................................................................................................................. 37
Figure 3. 11: CFD model ......................................................................................................... 38
Figure 3. 12: Mesh model for CFD model without fibers ....................................................... 39
Figure 3. 13: Inlet and Outlet boundary condition ................................................................... 40
Figure 3. 14: Symmetry boundary condition ........................................................................... 40
Figure 3. 15: Interior boundary condition ................................................................................ 40
Figure 3. 16: Porous cell zone.................................................................................................. 41
Figure 3. 17: Flowchart for generating 3D random fibers ....................................................... 45
Figure 3. 18: Random fibers developed in the porous zone .................................................... 46
Figure 3. 19: Mesh generated for fiber model ......................................................................... 48
Figure 3. 20: Element edges with curvature normal angle. ..................................................... 48
Figure 3. 21: Fibers set with ‘TRAP’ Boundary condition ...................................................... 49
Figure 4. 1: Pressure drop vs Velocity for Flat and Pleated Element ...................................... 52
Figure 4. 2: Equation from the experimental result of Flat sheet ............................................ 53
Figure 4. 3: Pressure drop when velocity is 0.00296 m/s ........................................................ 54
Figure 4. 4: : Pressure drop when velocity is 0.00591 m/s ...................................................... 55
Figure 4. 5: Pressure drop when velocity is 0.00887 m/s ....................................................... 55
Figure 4. 6: Experimental vs CFD with 5% error for flat sheet ............................................... 56
Figure 4. 7: Pressure drop vs velocity from the experiment .................................................... 57
Figure 4. 8: Pressure drop-Oil and water simulation for velocity of 0.0001773 m/s .............. 58
Figure 4. 9:Pressure drop-Oil and water simulation for velocity of 0.0001773 m/s ............... 58
Figure 4. 10: Pressure drop-Oil and water simulation for the velocity of 0.000709 m/s......... 58
Figure 4. 11: Experimental and CFD results ........................................................................... 59
Figure 4. 12: Discrete phase concentration on the fibers ......................................................... 61
List of Tables
Table 1. 1: Specification of the selected duplex filter ............................................................... 2
Table 2. 1: Capture efficiency Vs Beta ratio for any particle size (X) .................................... 25
Table 3. 1: Specification of Multipass test............................................................................... 30
Table 3. 2: Media layer specifications ..................................................................................... 31
Table 3. 3: Test matrix for the pleated element ....................................................................... 32
Table 3. 4: Test matrix ............................................................................................................. 34
Table 3. 5: Instruments and its specifications from manufacturers ......................................... 35
Table 3. 6: Study matrix........................................................................................................... 36
Table 3. 7: Oil Specification .................................................................................................... 42
Table 3. 8: Simulations ............................................................................................................ 42
Table 3. 9: Domain details ....................................................................................................... 44
Table 3. 10: Fiber details ......................................................................................................... 44
Table 3. 11: Mesh quality for the Model ................................................................................. 47
Table 3. 12: Simulations- Case 2 CFD model with fibers ....................................................... 50
Table 4. 1: Pressure drop for Flat sheet ................................................................................... 51
Table 4. 2: Pressure drop for Pleated Element ......................................................................... 51
Table 4. 3: Viscous resistance coefficients .............................................................................. 54
Table 4. 4: Pressure drop for Flat sheet from simulation ......................................................... 55
Table 4. 5: Pressure drop from the water absorption test ........................................................ 56
Table 4. 6: Viscous resistance coefficient................................................................................ 57
Table 4. 7: Pressure drop from CFD simulation with fibers .................................................... 59
Table 4. 8: Experimental and Simulation results of water absorption test .............................. 60
1
1 Introduction
1.1 Background
Filtration is a part of the wider concept of contamination control. Any contamination in the
working fluid interferes with the intended functions of a fluid or the associated fluid system
component. Contaminants may be in the form of solids, liquids or gas. The mechanical
filtration is a process where the foreign matter is separated from the working fluid by means of
a porous material. A mechanical filter is often used to separate the particulate matter from the
pressurized liquid or gaseous flow. Here, the filtration happens through a porous material. On
the other hand, coalescers or absorbers are used to separate the liquid contamination from the
working liquid flows and gaseous flows. Amount of water contamination present in the oils
usually defines the type of filtration method; smaller the water in volume, absorption is the
method to use and coalescing if otherwise. The limit of the water contamination to choose a
specific filtration method is, however, application dependent.
A perfect working fluid without contamination is practically impossible to achieve. Even
before the system is first commissioned, it contains considerable contaminant particles left over
from the manufacturing process, assembly and transportation. The hydraulic fluid used in the
system also contains several pre-existing contaminants. Numerous sources of contamination
bring a variety of particulate content such as dust, water, and wear particles into the working
fluid which damage the system components including cylinders, seals, valves, pumps, etc. over
the time. As a result, the overall performance of the system decreases and ultimately it can
lead to catastrophic failure. As reported by Gorle (2019), more than 90% of the failures of
hydraulic systems are due to the presence of foreign matter in the hydraulic oil. Replacement
of damaged mechanical components is not only expensive but also adversely impacts the
operation or production life cycle. In many modern production environments, the combination
of extended operating periods and fast cycle times tend to increase the risk of hydraulic fluid
contamination (Hannifin, Parker, 2010)
1.2 Parker’s Duplex filter for water separation from hydraulic oil
The duplex filters of Parker, shown in Figure 1.1 are mainly used to separate the water
contamination from the industrial lube oil systems and medium pressure hydraulic systems as
well as fuel systems of the diesel engines. The filter unit has two bowls wherein the filtration
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and servicing exclusively happen in either of them so that an uninterrupted filtration process is
possible. The maximum allowable flow rate is 80 l/min. The porous medium of the filter
element is made of cellulose media. Other specifications of the filter are furnished in Table 1.1.
Figure1. 1: Duplex Filter (left), and the water absorption filter element (right)
SPECIFICATION
Duplex Filter Valves can be changed with
the open center position
Maximum Operating Pressure 30 bar
Operating Temperature [-20°C …+160°C]
Weight 15 Kg
Nominal Flowrate (30 Cst) 80 l/min
Table 1. 1: Specification of the selected duplex filter
1.3 Problem Definition
Almost every engineering practice has an action of filtration. Filtration plays a significant role
in ensuring the right cleanliness of the hydraulic oil in numerous applications such as hydraulic
controls which would possibly halt without it. As a worldwide business fragment, filtration is
assessed to reach USD 110.82 billion by 2024 and to develop at a compound yearly
development rate of 6.50% from 2018 to 2024 (Abetz, 2018). This filtration market remains
underneath the consumer’s radar in light of the fact that their purchase is generally not filters.
What the consumers buy are the beverages that have been filtered; they buy automobiles and
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mobile machines that contains dozens of filters. Also, in medical injections to jet engines, the
filters are an auxiliary, but very important component of the whole system. Filters in vehicles
upgrade the eco-friendliness and clean the cabin air. Filtration and separation solutions in the
industrial processes have thus a direct influence on the economy.
Achieving acceptable cleanliness levels in today’s machinery has been an active research area.
Several research institutes like IFTS (Institut de la Filtration et des Techniques séparatives)
have focused on successful capture and removal of water contaminants from the hydraulic oil
flows. Ideally, the filtration of water contamination from hydraulic oil should not interrupt the
oil flow and create no energy loss as the flow passes through the filter media. A finer media
pack for the filter element can guarantee a better filtration quality but leads to increased
pressure drop at the same time. To this end, a trade-off between the system design which is
easy and economical to develop and efficiency that meets the oil cleanliness requirement
should be realized.
Water as a contaminant is present in most hydraulic systems in noticeable concentrations due
to its affinity towards the other liquids. The usual locations which promote the water
contamination in hydraulic systems are typically the air breathers, heat exchangers, worn seals,
and new oil. The hydroscopic nature of hydraulic oils causes them to pick up the water particles
from humid air. In enough quantity, these water particles produce undesirable effects in a
system designed for other fluids. The severity depends on the degree of water dissolution,
entrainment, and emulsification of the hydraulic oil. Below the saturation level, water will be
completely dissolved in the other liquids and the range of saturation is between 100 to 1000
parts per million (0.001% to 0.1%) at room temperature. The saturation is higher at room
temperature. Water becomes entrained above the saturation level, which means that it takes the
form of relatively large droplets. This is also called as free-water. Sometimes these droplets
come together and then drop (precipitate) to the bottom of the host fluid.
1.3.1 Water is highly reactive
Water reacts chemically with fluids and additives to interfere with their functions. This shortens
fluid life and produces by-products which are harmful. In enough quantity, water can result in
undesirable mechanical effects such as changes in viscosity, loss of lubrication and poor system
response.
Without fluid analysis or control measures, water content probably will increase to the point
where these and other symptoms begin to appear.
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Figure1. 2: Water reacts chemically with the fluid and system components
(Source: chemistry.stackexchange.com)
1.3.2 Symptoms of water contamination are explained below
1.3.2.1 System response:
When the concentration of water reaches 1% or 2%, the hydraulic system response is affected.
Water will shift the viscosity of the fluid which changes the operating characteristics of the
system. When the influx is swift, poor system response could be the first indication that there
is the presence of water.
Cavitation is another problem of water in the fluid. Since the vapor pressure of water is higher
than the hydrocarbon liquids, even small amounts in the solution can cause cavitation in pumps
and other components. This occurs when water vaporizes in the low-pressure areas of the
components, such as the suction side of the pump. Vapor bubbles collapse on metal surfaces in
these areas and fatigue damage results. The characteristics of sounds can also be noticed.
Water’s reaction to antiwear additives and oxidation inhibitors can produce solid precipitates.
Or the water may act as an adhesive to cause small particles to clump together in a larger mass.
These sticky solids may slow down values spools or cause them to stick in one position or
another. Also, they may plug component orifices. In either case, the result could be an erratic
operation or complete system failure.
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Figure1. 3: Water changes the viscosity of an oil base fluid (Parker Corporation, 2019)
1.3.2.2 Evidence of fluid reactions
Due to churning or other mixing action, undissolved (free) water may be emulsified into very
fine droplets suspended in oil. This could make mineral base oils appear cloudy or milky.
Sometimes, entrained air can give a similar appearance, but discrete bubbles are usually visible
when there is a presence of air.
If free water is present and the system operates at temperatures below 32°F, ice crystals will
form. The ice crystals can plug component orifices and clearance spaces. In a hydraulic system,
this will cause slow and erratic response. In a lubrication system, these crystals can stop the
flow of lubrication through metering valves.
1.3.2.3 Chemical reactions
Combined with high operating temperature (above 140°F), water reacts and destroys zinc type
antiwear additives. For instance, Zinc dithiophosphate (ZDDO) is a boundary lubricant that
reduces wear in high-pressure pumps, gears, and bearings. When this additive is depleted,
abrasive wear accelerates rapidly. This will show up as a premature component failure and
other wear mechanisms.
An inspection of failed components can point to another type of water damage. Aluminum and
zinc alloys may have a whitish oxide coating. Bearing and gear surfaces may show signs of
pitting. These are the signs of corrosion damage. The water presence will shorten the long life
expectancy of bearing. Apart from corrosion, water will contribute to shorter component life
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by lowering viscosity, which reduced the thickness of the fluids lubricating film. When the film
drops below a critical thickness, wear increases rapidly.
1.3.2.4 Microbial growth
Prolonged water contamination can eventually lead to the growth of microbes in the system.
These microbes can include algae, bacteria, fungi, and yeast. A foul odor, the appearance of
slime and sediment in the reservoir, and the darkening of fluid may be the signs of microbial
growth. If the microbial growth is severe, the viscosity of the fluid may increase dramatically.
Unfortunately, by the time these symptoms appear, system components and the fluid may have
been severely damaged which could lead to major overhaul or replacement of the system.
1.3.2.5 Rapid plugging of filters
As we have seen water creates reaction products and increase wear particles in a fluid. This
places a heavy load on system filters. When properly selected, particle filters will remove these
harmful by-products. But the filters will get quickly become plugged, resulting in frequent
replacement of the element.
The above reasons and factors clearly state that water in oil can be very destructive in nature
and therefore, there is a need in completely removing the water, which is almost impossible.
But there is always new techniques and material of media developed for efficient removal of
these water droplets. The main goal of the project is to evaluate how these water droplets are
absorbed by the filter media using the Discrete Phase Model (DPM) in Ansys and validate with
the experimental results.
1.4 Objective
The objective of this research work is
1. To make preliminary laboratory measurements for the pressure drop across the filter
medium using Multipass testing protocol (ISO 16889)
2. To develop a CFD model for estimating the pressure drop across the porous medium
3. To generate a 3D random fiber distribution of the selected porous domain and explore
the possibilities of using the Discrete Phase Model for simulating the water absorption
in the fiber medium.
4. To make a comparative study of numerical and experimental results
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1.5 Scope
This thesis work is an applied research work based on the requirement of the industry and
addresses how CFD can be used to improve the water filtration in hydraulic oil. Out of different
water separation/filtration techniques, this research is limited only to absorption method using
a multi-layered cellulose media. The work considered the experimental measurements of
pressure drop across the filter medium to generate the flow resistance coefficients of porous
material using the Darcy-Forchheimer equation, which are then used to define the material
properties in the CFD simulations. While the numerical modeling of media pack in the form of
flat sheet is validated using the laboratory measurements, the full-scale pleated filter is not
modeled in this work due to time constraints. However, a correction factor based on the
measurements of flat sheet vs pleated filter is used to extend the numerical findings of flat sheet
filter media to the pleated filter.
The attempt of generating the multiphase flow through a microstructural porous media is made
in this study. To reduce the complexity of the investigation, only X fibers are created in the
geometry model. However, the effective porosity of the modeled medium is consistent with
the real product. Also, the number of water particles injected into the domain is limited to
approximately 1500 to reduce the CPU effort. The validation experiments considered only the
steady state inflow conditions, which is not the reality in industrial applications. The scope of
this work is pictorially presented in Figure 1.4. These numerical models can be further
improved, and the knowledge can be of help in enhancing the porous properties of the medium.
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Figure1. 4: Scope of the thesis
1.6 Conclusion
In this thesis, the focus is on liquid-liquid separation, where the water is filtered out from the
hydraulic oil flow. Water can be in dissolved, undissolved (free) or entrained in an oil.
Depending on the form of waters presence in the oil, there are different water removal methods
such has settling, centrifuging, coalescing, vaccum distillation, adsorption, and absorption.
This chapter presented the introductory remarks of the project including the problem definition,
objectives, and scope of this work. The project focuses on the water absorbing property of the
fiber media, where a huge knowledge is available a wide range of application possibility. The
next chapter will make a literature survey on the porous flows and phase separation, which is
critical for developing an acceptable research methodology.
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2 Literature Review
2.1 Introduction
This chapter will focus on the topics that can be utilized in developing a methodology to carry
out the thesis. Section 2.2 gives an overview of how a porous media is used in filtration
applications and its properties like porosity and permeability. Section 2.3 explains different
water separations concepts such as coalescence and absorption process which are important in
understanding the physics of water droplets in fluid flows. The dynamics of fluid inside a
porous structure is given by Darcy-Forchheimer law. The literature focuses on how this law
can be utilized in determining the flows through porous media. The law is further used in fluid
flow equations for developing a numerical model. The simulation is carried out with the help
of Ansys Fluent and is detailed in section 2.6 respectively. There are many standard
experiments developed to study the porous medium, but section 2.7.4 will focus on two
experiments that can be used in validating the CFD model.
2.2 Porous media
Porous media are encountered everywhere in our daily life, technology and nature. Some dense
rocks and some plastics, virtually all solid and semi-solid materials are ‘porous’ in varying
degrees. For a material to be porous it should exhibit the following properties:
1. The material must contain pores or voids, free of solids, imbedded in a solid or semi-solid
matrix.
2. It is permeable to a variety of fluids, i.e. the fluid should be able to penetrate through one
face of material and emerge on the other side of the material.
Porous materials have become critical in engineering and technological advancements. In
hydrology, it relates to water movement in earth and sand structure and petroleum engineering
which is mainly concerned with petroleum and natural gas exploration and production (Perm
Inc, 2018). Another major application of porous materials is filtration. As the name filtration
means the process used to separate solids from liquids or gases using a filter medium that allows
the fluid to pass through them but not the solid. Here the filter medium is one which functions
like a porous medium.
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2.2.1 Porosity
Porosity also called as a void fraction, is a measure of empty spaces in the material. It is given
by
Porosity = 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑣𝑜𝑖𝑑 𝑠𝑝𝑎𝑐𝑒
𝑇𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒
The resistance to the flow through the filter medium depends on the effective pore size. An
ideal medium is characterized by a mass of holes divided by the thinnest possible wall, thus
presenting the maximum open area through which the fluid flows. In practice, these holes
account for an only a small part of the surface. The exact proportion depends on the properties
of the raw material from which the porous medium is made (Purchas & Sutherland, 2011).
Therefore, care should be taken before choosing a medium for specific industrial operation,
because it may affect the capital and operating costs. The actual resistance to flow is a
combination of the porosity and permeability of the medium
2.2.2 Permeability
Permeability is the measure of material’s ability to allow the fluids to flow through it. The
permeability of a filter medium is a vital measure of its capability of filtration. It is usually
determined through the experimental investigation of pressure drop across the medium at
different flow rates. There are several expressions for the permeability of the filter media.
Constant thickness presumption is more commonly used when the porous medium is treated as
a flat sheet than characterizing the medium by its permeability coefficient. Air and water are
the two fluids that are mostly used in the assessment of permeability. The technique employed,
and data generated vary by two extremes; one is using a fixed rate of flow and observing the
corresponding differential pressure and the other is using a fixed pressure and observing the
time required for the flow of the specified volume of fluid. (Purchas & Sutherland, 2011)
The empirical expression for the permeability quantifies the flow rate per unit area under
defined differential pressure. The permeability coefficient of the medium 𝐾𝑝 is defined by the
Darcy equation, which reads
𝑃
𝐿=
𝑄𝜇
𝐴𝐾𝑝
11
where P is the differential pressure in Pa, L is the depth or thickness of the medium in m, Q is
the volumetric rate of flow in m3/s, 𝜇 is the kinematic viscosity in Ns/m2, A is the area in m2,
𝐾𝑝 is the permeability expressed in m2
2.3 Water separation concepts
A dispersion consists of two immiscible liquids, where the dispersed phase exists as droplets
in the continuous phase. In the case of water in oil, as concerned in this project, oil is the
continuous phase and water is the dispersed phase. An appropriate way of removing water from
the oil is usually chosen by the type of problems the contamination is causing. This is due to
the fact that the problem may be related to the water concentration and which determines the
suitability of the separation or filtration method. This section presents the popular methods –
coalescence and absorption of water from the oils.
2.3.1 Coalescence
Multiphase flows are associated with a multitude of interactions, which involve a collision
between the droplets and particles. When two or more droplets collide or in contact with each
other for a long time, the coalescence phenomena take place. A study on the dynamics of drop
coalescence has been revealed that the impact condition decides whether the drop will either
coalesce with another droplet or splash (Fedorchenko & Bang Wang, 2004). It can either form
a complete coalescence with a secondary droplet or may even form partial coalescence. Also,
the drop can bounce off or float on the liquid surface (Yong;Park;Hu;& Leal, 2001). On the
other hand, every collision does not lead to coalescence. When a drop comes in contact with
the surface of the same fluid, it floats on the interface for a finite time until the thin layer of the
surrounding fluid between the two interfaces drains out (Deka;Biswas;Chakraborty;& Dalal,
2019). The coalescence phenomena of two droplets are shown in Figure 2.1 where the thin film
is formed after a finite time.
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Figure 2. 1: Two droplets going to collide (Left) and Droplets forming a thin film after a
finite time (Right)
2.3.2 Absorption
Absorption is a physical and chemical phenomenon in which atoms, molecules or ions enter a
bulk phase, either liquid or solid material. In this process, the molecules are taken up by volume
by a liquid (absorbent, solvent).
In the context of filtration, filter medium absorbs the liquid contaminant. Absorption filter
media creates a process wherein the porous material draws the contaminant and retains it until
it gets saturated. Figure 2.2 demonstrates how a single fiber absorbs the water molecules in a
filter media.
Figure 2. 2: Process of water absorption by a cellulose fiber
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2.4 Water Absorption through Cellulose media
Cellulose is one of the popular porous materials. The hydrophilic fibers of the medium are
capable of absorbing the water particles and the pores will allow the oil through flow through
it. The pores of the medium trap the water and hold them 100 to 1000 times their weight in
water, and will allow the oil to pass through them. Absorption of water causes the fibers of the
cellulose paper to swell and the space between the adjacent fibers to reduce, this will cause the
restriction of the flow and rise in the pressure drop across the medium.
2.5 Darcy and Forchheimer law
Flow regimes are classified by the dimensionless quantity called Reynolds number (Re), which
is defined as
𝑅𝑒 =𝜌𝑣𝑙
𝜇
where 𝜌 is the fluid density (kg/m3), 𝑣 is the fluid velocity (m/s), 𝑙 is the characteristics length
(m) and 𝜇 is the fluid viscosity (Pa s).
Refer to Figure 2.3 the flow regimes in porous media are classified as lower Re to higher Re
(Skjetne & Auriault, 1999).
Figure 2. 3: Flow regimes in porous media (Skjetne & Auriault, 1999)
1=Darcy
2=weak inertia
3=Forchheimer (strong inertia)
4=transition from Forchheimer to turbulence
5=Turbulence
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Darcy (Darcy, 1856) developed a one-dimensional empirical model for laminar flow through
porous media at low flowrates (Re < 1). The pressure gradient and the flow rate have a linear
relationship and it assumes that the viscous forces dominates the inertial forces in the porous
medium. Therefore, the inertial forces can be neglected. Darcy’s equation is given below:
−∇𝑝 =𝜇
𝛼 𝑣
Where 𝑣 is the velocity of the fluid in a porous media, 𝛼 is the permeability of the porous
medium, 𝜇 is the dynamic viscosity of the fluid, ∇𝑝 is the pressure drop in the flow direction.
The law is a standard approach to describe single-phase flow in microscopically disordered and
macroscopically homogenous porous media (Costa, 1999). This law is only valid for flows
with low Reynolds number, such as laminar flows.
Forchheimer equation is a phenomenological approach. It was seen that Darcy’s law deviates
for Re numbers of around 10. For turbulent flows in porous media, both the viscous and inertial
effects cause more non-linear behavior which has to be considered. Forchheimer then added a
term in Darcy’s equation in order to account for this non-linearity. This equation which he
developed is accepted as an extension to Darcy’s equation for higher flow rates. As the flow
rate (Reynolds number) increases, the pressure drop transforms from Darcy regime to
Forchheimer (strong inertia) regime. Therefore, we have
−∇𝑝 =𝜇
𝛼 𝑣 + 𝛽𝜌𝑣2
Where 𝛽 is the inertial resistance(coefficient) or non-Darcy flow coefficient or Forchheimer
coefficient (1/m) and 1
𝛼 is the viscous resistance coefficient.
This viscous resistance coefficient and inertial resistance coefficient are added as a momentum
source term to the standard fluid flow equations during the simulation for a porous media.
2.6 Computational Fluid Dynamics (CFD)
Computational Fluid dynamics (CFD) is used to analyze systems involving fluid dynamics,
heat transfer and various other related phenomena by numerical calculations. It has larger
applications in both industrial and non-industrial applications. In this thesis, Ansys fluent is
used for simulation.
15
Generally, a flow can be described by solving the three consecutive equations:
• Conversation of mass
• Conservation of momentum
• Conservation of energy
For incompressible flows, the equations for conservation of mass and momentum are referred
to as Navier-Stokes equation which is partial differential equations (PDEs) and difficult to
solve analytically. A discretization method that approximates the PDEs with a system of
algebraic equations is applied and solved numerically on a computer. These algebraic equations
are then solved for small domains in space and time. The numerical solution of the flow consists
of a solution in these discretized locations. The accuracy of the solution is very much dependent
on the discretization method used.
The CFD simulation has many advantages in engineering analysis. It is a useful tool to analyze
the flow characteristics when experiments are very costly. But, we need to understand that the
CFD simulations are an approximation of real experiments and should not be considered as a
substitute for experiments, but rather it should be complimentary to experiments.
Governing equations for the continuous flow
The general form of the mass conservation equation or continuity equation is given by
𝜕𝜌
𝜕𝑡+ ∇. (𝜌�⃗�) = 𝑆𝑚
𝑆𝑚 is the mass added to the continuous phase from an eventually dispersed second phase. The
continuity equation for incompressible flow can be simplified to
∇. (�⃗�) = 𝑆𝑚
Momentum conservation equation is given by
(𝜕
𝜕𝑡(𝜌�⃗�) + ∇. (𝜌�⃗��⃗�)) = −∇𝑝 + ∇. 𝜏̅ + �⃗�
Where �⃗� is the external body forces while 𝜏̅ is the stress tensor
𝜏̅ = 𝜇 [(∇�⃗� + (∇�⃗�)𝑇) −2
3. ∇. 𝑣⃗⃗⃗⃗ 𝐼]
16
The energy equation can be expressed as:
𝜕(𝑇)
𝜕𝑡+ ∇. (�⃗�𝑇) = ∇(𝛼∇𝑇) +
1
𝜌𝑐𝑣
(𝜏̅. ∇). �⃗�
Here, 𝛼 =𝑘
𝜌𝑐𝑣 is the thermal diffusivity. The energy equation for incompressible flow is
decoupled from Navier Stokes equations. This means that the mass conversation and
momentum conservation equation are solved first for 𝑣 ⃗⃗⃗ ⃗ 𝑎𝑛𝑑 𝑝 and then for energy equation
for T.
2.6.1 Multiphase flow
The flows in nature can be of a mixture of phases that are gas-liquid, gas-solid, liquid-solid or
liquid-liquid flows or also can be a more complex with a mixture of three phases as gas-liquid-
solid flows. In our case, the focus is on two phases that is liquid-liquid phase flows, where oil
is considered as the continuous phase and water is a secondary phase. The secondary phase
volume fraction is low, for this different model are considered below and an appropriate one
which is most equivalent to the case is considered.
There are two basic methods for multiphase phase flow simulation.
1. Eulerian-Eulerian Approach
2. Eulerian-Lagrangian approach
Figure 2. 4: Overview of the modeling approaches (Tsuji, 2008)
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2.6.1.1 Eulerian Approach
In this approach, different phases are treated mathematically as interpenetrating continua and
are based on the fact that space can only be occupied by a single phase at any one time i.e. total
volume fraction of all the phases are equal to 1. There are several variations in this method
which are listed below.
2.6.1.1.1 VOLUME OF FLUID MODEL
It is a method studied and developed by (Hirt and Nicholas, 1981) and it is a used to model two
or more immiscible fluids by solving a single set of momentum equation and tracking the volume
fraction of each of the fluids throughout the domain.
2.6.1.1.2 MIXTURE MODEL
The mixture model is like VOF model, uses a single fluid approach. But it differs from VOF in
two aspects that is the mixture model allows the interpenetrating of phases, therefore, the volume
fraction for two phases in a control volume can be equal to any volume between 0 and 1. The
mixture model allows the phases to move at different velocities using the concept of slip
velocities. Here, one momentum equation is solved for the n-phases during transportation.
2.6.1.1.3 EULERIAN MODEL
It allows modeling of multiple, yet separate phases. This model, the number of secondary phases
is limited only by memory and convergence behavior. Any number of secondary phases can be
modeled provided there is enough memory is available. In this model ‘N’ momentum equation
is solved for the n-phases during transportation. This model is used when the volume fraction of
the secondary phase is more than 10%.
2.6.1.2 Eulerian-Lagrangian Approach- Discrete Phase model
In this approach, the oil is considered as continuous phase whereas the secondary phase that is
the water liquid is tracked as a discrete particle using the application of Newton’s laws of
motion. In this project, we will look into the Eulerian-Lagrangian approach based on the fact
that the volume fraction of water droplets in oil is less than 10 % and there is limited interaction
with continuous flow. When the volume is low, the force balance for each particle is solved
individually and computational power has to be made. The trajectories of the particles/water
droplets are computed in the Lagrangian reference frame.
18
The force balance on a single particle derived from Newton’s law:
ⅆ𝑣𝑝⃗⃗⃗⃗⃗
𝑑𝑡= 𝐹𝐷(𝑣𝑐⃗⃗ ⃗⃗ − 𝑣𝑝⃗⃗⃗⃗⃗) +
𝑔(𝜌𝑝 − 𝜌)
𝜌𝑝+ 𝐹𝑖
𝐹𝐷 is the drag force which is the function of relative velocity
𝐹𝐷 =18𝜇𝐶𝐷𝑅𝑒𝑟𝑒𝑙
𝜌𝑝𝑑𝑝224
The drag coefficient 𝐶𝐷 can be considered to be a single most important force acting on the
discrete phase. Water droplets attain a spherical shape due to surface tension, and for spherical
particles, the Morsi and Alexander drag law (Morsi & Alexander, 2006) is considered. This
drag law is as follows
𝐶𝐷 = 𝑎1 +𝑎2
𝑅𝑒𝑟𝑒𝑙+
𝑎3
𝑅𝑒𝑟𝑒𝑙2
In the above equations, 𝑣𝑐⃗⃗ ⃗⃗ the velocity of the continuous fluid phase, 𝑣𝑝⃗⃗⃗⃗⃗ 𝑡ℎ𝑒 velocity of the
particle, 𝜇 is the molecular viscosity of the fluid, 𝜌 is the density of fluid, 𝜌𝑝 is the density of
the particle, 𝑑𝑝 is the diameter of the particle, 𝑔(𝜌𝑝−𝜌)
𝜌𝑝 is the gravity force, 𝑅𝑒𝑟𝑒𝑙 is the relative
Reynolds number, defined by:
𝑅𝑒𝑟𝑒𝑙 =𝜌𝑑𝑝(𝑣𝑝 − 𝑣𝑐)
𝜇
The force balance equation also includes additional forces, called 𝐹𝑖. The additional forces are
important in certain times among these are Virtual mass force, which is the force required to
accelerate the fluid surrounding the particle and another is the additional force that exits
because of the pressure gradient in the fluid. Both forces are important when 𝜌 > 𝜌𝑝 . The
additional forces can also include Saffman lift force, Brownian motion, Collision, Break up.
2.7 Research methods
2.7.1 Computational methods
Ansys fluent has a CFD tool can be used to simulate the pressure drop and also analyze the
water absorption process. Since both these characteristics are essential in the present work, an
insight is given for different models.
19
2.7.1.1 Porous modeling in the fluent
Fluent has inbuilt porous media conditions that can be used for a variety of single and
multiphase problems. This condition can be utilized for packed beds, filter papers, perforated
plates, flow distributions and tube tanks (Fluent, 2019). This model is activated only for the
cell zones in which a porous media model is applied and the pressure loss in the flow is
determined by the addition of momentum source term in standard fluid flow equation. The
viscous resistance coefficient and inertial resistance coefficient are considered based on the Re
number. If the viscous forces are dominant, then we neglect the inertial resistance coefficient.
In fluent this resistance coefficient are defined using a cartesian coordinate system where it
defines two direction vectors for 3D and then specify the viscous and/or viscous resistance
coefficient in each direction.
In 3D there are three possible categories of coefficients:
• For isotropic material, the resistance coefficients in all directions are the same and
hence the same values are set in each direction. For example sponge
• When the resistance coefficient in two directions are the same and third direction is
different. Here the values are to be set accordingly for each direction. For example, if a
porous region consists cylindrical straws with small holes in them which are positioned
parallel to the flow direction, the flow would easily pass through the straws, but the
flow in the remaining two directions (through the small holes) would be very little.
• The third possibility is that the coefficients are different in all three direction
These values can be calculated from the experimental data that is available in the form of
pressure drop against velocity through the porous region.
Another important factor that is to be included is the porosity. That is usually in the range of 0
to 1 in fluent. The porosity 𝛾 is the volume fraction of the fluid within the porous region (that
is, the open volume fraction of the medium). The value of 1 describes that the medium is
completely open (no effect of the solid medium). Different material has different porosities
which are to be determined set during the simulation.
2.7.1.2 Discrete Phase modeling (DPM)
The discrete phase model (DPM) in fluent can be used in solving the multiphase problem which
allows simulating a discrete second phase in a Lagrangian frame of reference. This secondary
20
phase consists of the spherical or non-spherical particle (which may be taken as bubbles or
droplets) dispersed in a continuous phase. Fluent has the ability to compute the trajectories of
these discrete phase entities as well as heat and mass transfer to/from them. It can also include
coupling between the phases and its impact on both the discrete phase trajectories and the
continuous phase.
2.7.1.2.1 INJECTION OF PARTICLE OR WATER DROPLETS IN DPM
Water droplets are can be injected into the flow based on the initial conditions of the water
droplet properties. The properties of the water droplets usually include position (x, y, z
coordinates of the particle), velocities (u, v, w) of the particle, the diameter of the particle, the
temperature of the particle and mass flow rate of particle steam that will follow the trajectory
of the individual droplet.
The injections can be from a single point, group or from a surface. Fluent provides a variety of
injection type which can be incorporated based on the desired injections.
Figure 2. 5: Droplet distribution defining an initial spatial distribution of particle streams
(Fluent, 2019)
2.7.1.2.2 BOUNDARY CONDITIONS IN DPM
The fluent’s DPM boundary condition is important in modeling the water absorption process.
Generally, when the particles reach the physical boundary eg: a wall or inlet boundary, fluent
determines the fate of the trajectory at the boundary based on applied discrete phase boundary
condition. These boundary conditions can be defined separately for each zone in the fluent
model.
21
Types of boundary conditions are:
1. Reflect- Rebounds the particle off the boundary by a change in momentum which is
defined by the coefficient of restitution. The normal coefficient of restitution defines
the amount of momentum in the direction normal to the wall that is retained by the
particle after the collision with the boundary (Fluent, 2019).
𝑒𝑛 =𝑣2,𝑛
𝑣1,𝑛
Where, 𝑣𝑛 are the particle velocity normal to the wall and the subscripts 1 and 2 refer
to before and after the collision, respectively.
Figure 2. 6: Reflect Boundary condition in fluent for discrete phase (Fluent, 2019)
2. Trap- This condition terminates the trajectory calculations and records the fate of the
particle as ‘trapped’. This can be utilized in water absorption of cellulose fiber. The
mass of water droplets deposited can be easily determined on the fibers and can be
utilized for studying the distribution, material, and diameter of fibers in the cellulose
media.
Figure 2. 7: Trap Boundary condition in Fluent for discrete phase (Fluent, 2019)
22
3. Escape- This boundary condition reports that the particle as having ‘escaped’ when
it encounters the boundary in question. In this boundary condition, the trajectory
calculations are terminated.
Figure 2. 8: Escape Boundary condition in Fluent for discrete phase (Fluent, 2019)
4. Interior- These are used when the particles have to be passed through the internal
boundary and are available for only internal boundary zones.
2.7.2 Turbulence modeling
The simulation must use a laminar or a turbulent model, which is to be decided based on the
flow regime. Turbulence modeling is more computationally expensive. The choice of
turbulence model is based on flow characteristics and regime, geometry and computational
time.
Turbulent flows are characterized by random and chaotic variance in velocity and other flow
properties. These flows also contain rotational flow structures with turbulent eddies. The larger
eddies are dominated by inertial effects. This leads to that turbulent flows have a higher amount
of inertial forces compared with laminar flows (Versteeg & Malalasekera, 2007)
Reynolds number is used to determine whether the flow is laminar or turbulent. It gives the
relative importance between the inertia forces acting on a fluid and viscous forces (Versteeg &
Malalasekera, 2007).
The simplest and ‘complete model’ of turbulence are the two equation in which the solutions
of the two separate transport equation allows the turbulent velocity and length scales to be
independently determined. There are several two-equation models that can be used like k-
epsilon, k-omega, and RSM which are utilized in most practical engineering flow simulations.
23
2.7.3 Fluent solver
The phase coupled SIMPLE algorithm can be used to couple the pressure and velocity
equations in our model. The SIMPLE algorithm uses a relationship between velocity and
pressure corrections to enforce mass conservation and to obtain the pressure field. Also, the
discretization methods approximate the differential equations that are solved by the computer.
In order to obtain numerical solutions for governing equations, discretization methods are
implemented. The accuracy of the solution is dependent on the discretization.
First order and second order upwind schemes are the recommended discretization schemes.
The practical difference between these two is the truncation error, which is the difference
between the exact equations and the discretized equations. The truncation error is reduced in a
second order scheme because more cells faces are taken into interpolation. The accuracy is,
therefore, higher for second order scheme than for a first-order scheme, which may also
introduce a high level of diffusion. For this simulation, the discretization of momentum,
turbulent kinetic energy, and specific dissipation rate was done using the second order upwind
method.
Under-relaxation factors are used to control the update of computed variables at each iteration
(Fluent, 2019). This will assist in stabilizing the convergence. If any unstable behavior occurs,
the under-relaxation factors can be reduced.
2.7.4 Experimental methods
2.7.4.1 Single pass and Multi-pass test method
Any porous material or filter elements when developed is tested for its efficiency and
contaminant holding capacity and, in the meantime, not increasing the pressure drop. There are
many efficiency tests that were developed, but there are two tests which are commonly used in
industries, which are the single pass and multiple pass test (ISO, 2008). One simulates the
single pass system and another test the circulating fluid system. In a single pass test, a fluid
volume with a known amount of standard contaminants passes through the test elements only
once. Fluid particle counters determine contamination concentration upstream and downstream
of the element for various particle sizes.
The other test is the Multipass Test Procedure-ISO 16889, where the filtration industry uses it
to evaluate the filter element performance. In this test, the test procedures simulate what
24
happens to a fluid circulating a system. This test creates a realistic mathematical model for
circulating filtration systems. Also, it creates data set for filter elements that can give the
contaminant removal efficiency, contamination holding capacity and differential pressure
rating for any kind of filter being tested. The data set can be used to compare filter elements,
new filter material or media layers and filter housing design. Such comparisons are helpful in
making product selections and thus making designers select cost-effective filter media for their
systems.
Both the tests are to be set with some standard variables and changing these variables can
change the test results for any given element. The standard variables are given below:
• Temperature/viscosity,
• Upstream contamination concentration
• Flow rate and density
• System volume and mass of contamination passed through the filter
• The differential pressure across the element at which the test is ended
The data obtained can be used to calculate the filtration beta ratios. Filtration ratios can be used
to express the fraction of the particles getting through the element and is calculated as described
below.
Beta(X) = No of particle ≥𝑠𝑖𝑧𝑒 (𝑋)upstream
No of particle ≥𝑠𝑖𝑧𝑒 (𝑋)downstream
The table 2.1 illustrates the Beta ratio for any particle size and its corresponding efficiency.
This table can be used for any particle size, and the diameter of the particle in micrometers
would replace the ‘X’ in Beta (X).
Beta (X) Efficiency %
1.0 0.00
1.5 33.33
2.0 50.00
4.0 75.00
10.0 90.00
20.0 95.00
50.0 98.00
75.0 98.67
25
100.0 99.00
200.0 99.50
1000.0 99.90
5000.0 99.98
Table 2. 1: Capture efficiency Vs Beta ratio for any particle size (X)
2.7.4.2 Water absorption test
There are no widely accepted tests methods that are recognized or published by the standard-
setting organization for testing the water removal elements. Testing labs usually use Single
pass and Multipass test methods for water absorption to test and rate the water removal
elements. Thus, the manufacturers are free to establish and develop their own test methods.
Most of the laboratories use the Karl Fischer titration method to measure the water content in
the fluid.
A known quantity of water is fed into the system at a known flow rate using a peristaltic pump.
The water-laden fluid is pumped through a test filter using a gear pump followed by a
centrifugal pump to emulsify the water into the oil. The differential pressure is monitored and
the filtered fluid is returned to the reservoir.
Capacity and Efficiency can be calculated using the below formula:
Capacity C = 𝑾𝒇𝒆𝒅 − 𝑾𝒓𝒆𝒎𝒂𝒊𝒏𝒊𝒏𝒈
Efficiency % = 𝑾𝑪𝒂𝒑𝒕𝒖𝒓𝒆𝒅
𝑾𝒇𝒆𝒅 X 100 %
Where C is the Capacity
E is the Efficiency
𝑊𝑓𝑒𝑑= Mass or Volume of water feed
𝑊𝑟𝑒𝑚𝑎𝑖𝑛𝑖𝑛𝑔= Mass or volume of water remaining
𝑊𝑐𝑎𝑝𝑡𝑢𝑟𝑒𝑑= Mass or volume of water absorbed
2.8 Conclusions
It is evident that porosity and permeability are the two main factors that characterize a porous
medium. The one-dimensional empirical model for laminar flow through porous media by
26
Darcy is used in developing the numerical model. The necessary inputs to the model can be
calculated from experiments and thus helping in validation of the numerical results.
Computational Fluid Dynamics has the capabilities to estimate the pressure drop and amount
of water deposited on the fibers of the filter media. Ansys Fluent is used for this purpose, where
Darcy’s law is added to the standard fluid flow equation that results in pressure variations for
the considered cell zones and DPM model is used in simulating the water absorption process.
From the above literature study, a research methodology is developed that is used in estimating
the pressure drop and water absorption for the considered filter element.
27
3 Methodology
3.1 Introduction
The methodology is developed based on the literature study of various experiments and fluid
flows relating to the porous medium. There are two experiments which are to be conducted,
one is the pressure drop test by Multipass method and other is the water absorption test. The
experiments are conducted at Parker’s R&D lab. The first experiment measures the pressure
drop and other experiment measures the water content absorbed for the considered filter media.
The experiments are detailed in section 3.2 and 3.3 respectively. CFD models were generated
based on the media used in the filter element. Two models were developed that are illustrated
in sections 3.4.1 and 3.4.2 respectively. Figure 3.2 shows the detailed methodology flowchart
adopted in the project.
29
3.2 Pressure drop tests using Multipass method
The multipass test is used for providing the information of differential pressure across the
element. A Schematic diagram of the experimental system is shown in figure 3.2.
In this project, the test is used for measuring the pressure drop for flat sheet and pleated
element. There is no information or data related to contamination removal efficiency or
contamination holding capacity as the contaminants are not added. It will only focus on the oil
flow through the flat sheet and pleated element which results in differential pressure for
different flow rates. From this experiment, a correction factor is determined that is used in
calculating the viscous resistance coefficient. This coefficient is used in porous modeling
during CFD simulation. Figure 3.3 and Table 3.1 shows the Multipass test bench and its
specifications.
Figure 3. 2: Schematic diagram of Multipass test bench
30
Figure 3. 3: Multipass test bench
ISO 16889
Flow 15-30 l / min
60-300 l/min
Max Δp 20 bar
Test options 1. Pleated element
2. Flat sheet option
Table 3. 1: Specification of Multipass test
The oil flowing through the flat sheet is much faster when compared to the pleated elements.
In flat sheet, the pores are much more prominent by which the majority of the contaminants
smaller than the pore size just pass through it. The filtration area is minimum and thus the
pressure drop is less. But in the case of pleated elements, the filtration area is very larger, and
flow is subjected to longer filtration time when compared to a flat sheet. The pores are oval at
the bends of the pleats causing more restrictions in flow. Hence, there is an increase in pressure
drop. In order to understand this phenomenon, the multipass test was carried out for flat sheet
and pleated element which are detailed in upcoming sections.
31
3.2.1 Test 1: Pleated element
Pleated element in hydraulic fluid flow system provides a greater surface area and has a greater
capacity to capture and retain particles. The design of pleat numbers and pleats height in the
unit length greatly impacts the pressure drop in the filtration process (Hai Ming Fu, 2014).
The pleated element is a water absorbing type of filter element that is used inside the DF2145
filter. It consists of 57 pleats with an effective height of 317 mm. The pleated media is
composed of six layers of media which are shown in Figure 3.4 and its specification is shown
in Table 3.2.
Figure 3. 4: Layers in the filter element
Fiber orientation Type Thickness in mm
Layer 1 Glass fiber 0.24
Layer 2 Cellulose fiber media 1.3
Layer 3 Cellulose fiber media 1.3
Layer 4 Solid filtering 0.46
Layer 5 Non-woven 0.24
Layer 6 Metal mesh 0.1778
Total thickness 3.7178
Table 3. 2: Media layer specifications
32
The experiment is conducted to estimate the pressure drop occurring due to the oil flow through
the pleated element. The experiment is started by maintaining the temperature of the oil at 40°C
whose viscosity is found to be 15 Cst. The pump used to circulate the oil is set in such a way
that the desired flow rates are obtained, refer to Table 3.3. The experiment is repeated for 5
times, so there is consistency in the reading and the average pressure drop is taken into
consideration. The results are compared with the flat sheet values that are detailed in section
4.1. Figure 3.5 shows the housing used for the pleated element.
Figure 3. 5: Housing used for Pleated element in the test rig
Flowrate
l/min
Viscosity
Cst
Density
𝑘𝑔/𝑚3
Temperature
°C
Operating
pressure
Pa
50 15 870 40 500000
100 15 870 40 500000
150 15 870 40 500000
Table 3. 3: Test matrix for the pleated element
33
3.2.2 Test 2: Flat sheet
The flat sheet is cut from the actual pleated element. The pleats are straightened and made flat.
It contains the exact six layers that are used in the pleated element whose function is to capture
the contaminants like dust, metals, water droplets, etc. The flat sheet containing the six layers
is cut exactly in 0,189 m in diameter and placed on the testing rig. Figure 3.6 and Figure 3.7
shows the flat sheet and housing used for flat sheet in the test bench.
Figure 3. 6: Flat sheet and its layer orientation used for pressure drop test
Figure 3. 7: Housing used for flat sheet in the test bench
The pressure drop from the flat sheet is comparatively less when compared with the pleated
element which is determined using the experiment. The experimental condition is not changed,
and the oil temperature and viscosity are maintained at 40°c and at 15 Cst. The maximum
pressure drop for a flat sheet of area 0.0282 m2 is less than 5 bars, therefore, the flow rates are
34
reduced in this case. The experiment is repeated for 5 times, so there is consistency in the
reading and the average pressure drop is taken into consideration. The results are compared
with the pleated element values that are detailed in section 4.1. Table 3.4 shows the test matrix
for the flat sheet media.
Flowrate
l/min
Viscosity
Cst
Density
𝑘𝑔/𝑚3
Temperature
°C
Operating
pressure
Pa
5 15 870 40 500000
10 15 870 40 500000
15 15 870 40 500000
Table 3. 4: Test matrix
3.3 Test bench for water absorption from hydraulic flows
Water absorption test is used to determine the water absorbing properties of a filter element.
This setup is specially designed and used when water is a major contaminant in the hydraulic
oil flow. The experiment will yield pressure drop, water absorption capacity, time and
efficiency of filter media. The results are used for comparison and selection of the type of water
absorber, media layer specification for specific water absorption operation.
This test setup was built in house at Parker’s R&D lab and is based on the multi-pass
arrangement. The setup contains a free circuit and a test circuit. In the free circuit, oil is in
continuous circulation in the system and the test circuit is where the filter element is placed for
testing. The reservoir tank stores and supplies the oil in the system. The setup also contains a
small water tank to supply water into the oil. A temperature sensor is used to record the
temperature of the oil. Pressure, water content and flow measurements are also noted by the
system for continuous monitoring. Water content in an oil is measured using an Oilan water
analyzer device that instantaneously shows the changes in the lubrication oil’s water content.
A Schematic diagram of the experimental system is shown in Figure 3.8. Table 3.5 shows the
instruments and its uncertainty from the manufacturers.
35
Figure 3. 8: Schematic diagram of the experimental system of water absorption test
No Instruments Specification Uncertainty
1 Oilan (water in oil analyzer)
0-5000 ppm ±30 ppm
2 Flow meter on free and test
circulation 0- 300 l/min ±2 %
3 𝛥𝑃 measuring device
0 to 200000 Pa ±0.5%
4 Pump 0-300 l/min -
Table 3. 5: Instruments and its specifications from manufacturers
Before the test is started, we know that every hydraulic oil will contain a small amount of solid
and liquid contaminant in the form of metals, dust, sand particle, water, etc. These solid
contaminants are removed prior to the test by using a filter designed to remove the solid
36
particles. When maximum particles are removed, the setup is changed to test circuit. This is
done so the solid particles will not influence the pressure drop during the water absorption
process.
The test is started by adding 200 ml (0.2 kg) of water into 20-liter oil reservoir tank (volume
of water in oil is 0.01%) and allowing it to mix for about 30 minutes. The test circuit is then
opened were oil and water start flowing through the water absorbing filter element. The filter
element starts absorb the waters molecules and reduce the water content in the oil. The
experiment is monitored until there is no further drop in water content in the system. The test
is carried out for different flow rates and corresponding pressure drop and water content values
are noted. Table 3.6 shows the study matrix of the experiment.
Flowrate
l/min
Viscosity
Ns/𝑚2
Density
𝑘𝑔/𝑚3
Temperature
°C
Initial water content
ml
Operating
pressure
Pa
5 0.02784 870 40 200 500000
10 0.02784 870 40 200 500000
20 0.02784 870 40 200 500000
Table 3. 6: Study matrix
3.4 Computational framework
CFD is a well-established tool which can be utilized to study the water absorption in a cellulose
porous media. Firstly, the necessary domain or CAD required to simulate the pressure drop
across a porous media is created using Ansys workbench. The model is further developed with
random fibers that are distributed over its porous zone. The model is then discretized with
appropriate element size and the necessary boundary conditions, physics models are set. The
study does not include any temperature effects; thus the energy equation is not considered. The
mass and momentum equations are then solved using pressure-based solver using SIMPLE
algorithm. A schematic of the general setup is shown in Figure 3.9.
Figure 3. 9: Schematic of the general CFD setup.
Geometry
•Computer Aided Design
Meshing
•Flow geometry is divided into cell
Physics
•Flow and Boundary conditions are setup
Solve
•Flow equations are solved
Post-Processing
•Assessment of flow variables
37
There are two cases which are detailed in the upcoming sections, one is the flow of only oil
through a porous domain which gives a pressure drop and is validated with the pressure drop
test using Multipass method. The second case involves the development of fibers in the porous
domain with a thickness equal to the cellulose water absorber media which is validated using
the water absorption test.
3.4.1 Case 1: Model without Fibers
3.4.1.1 Geometry
The filter contains six layers of media whose thicknesses are equal to 3.717 mm and the overall
length and slighting width of the water absorber media is as shown in Figure 3.10. To make
simulation much easier and faster, only 1/50th of its length and width is considered.
Figure 3. 10: Pleated media stretched to the flat sheet and the size considered for CFD
modeling
The rectangular model of 29.64 mm X 6.34 mm with the overall domain length of 10.717 mm
is created and the model contains three fluid zones that are inlet zone, porous zone and outlet
zone which are of 3 separate bodies, refer Figure 3.11. The six layers of the media which are
3.717 mm in thickness is considered as a single layer with a porosity of 0.9 (from the datasheet
of the material manufacturer) and is represented as a porous zone in the model. This is done as
the model is only used for getting the pressure drop across the porous media with different flow
rates of oil only. The simulation does not include any water absorption phenomenon.
38
The three bodies inlet, porous and outlet have a contact region between each other. These
contact regions are important while carrying out a 1D simplification of porous media model
available for cell zones, which acts as a porous jump type wall condition. But in our case, it is
a 3D model, where the cells are considered as porous zone, and the inlet and outlet face of the
porous zone is considered as interior faces of the zones.
To eliminate the contact region and defining the inlet and the outlet faces of the porous zone
as interior, the geometry containing 3 bodies is formed as one part. Ansys workbench is used
in order to carry out the modeling.
Figure 3. 11: CFD model
39
3.4.1.2 Mesh Generation
The CFD model is a simple rectangular geometry with no complex joints or shapes which
makes mesh generation quite simple and easier. In Ansys, one can choose a global element
order option that allows controlling whether meshes are to be created using midside nodes
(quadratic elements) or without midside nodes (linear elements). Due to the simple 3D model,
the linear element is considered, where meshes are created without midside nodes and with an
element size of 0.5 mm.
The quality of mesh plays an important role in the accuracy and stability of the numerical
computation. Three factors are important for having a good cell quality which are Orthogonal
quality, Aspect ratio, and the Skewness. Due to the simple model, these parameters are well
within the desired values. The mesh model is shown in Figure 3.12
Figure 3. 12: Mesh model for CFD model without fibers
3.4.1.3 Boundary Conditions and Cell zone
The velocity inlet was specified at the inlet where the oil starts its flow and the outlet was
specified to be pressure outlet boundary condition, refer Figure 3.13. The cells in inlet and
outlet fluid zones are considered as an interior. The shortest faces of the inlet, porous, outlet
fluid zone is considered as a symmetry boundary condition, refer Figure 3.14. The remaining
surfaces are considered as walls.
The inlet and outlet faces of the porous zone which act as a boundary between the porous and
non-porous zone are also considered as the interior, refer Figure 3.15. The porous cell zone
represents the porous medium and creates resistance to flow. Figure 3.16 shows the cells of
porous media.
40
Figure 3. 13: Inlet and Outlet boundary condition
Figure 3. 14: Symmetry boundary condition
Figure 3. 15: Interior boundary condition
41
Figure 3. 16: Porous cell zone
3.4.1.4 Turbulence model
The simulation is performed using Ansys Fluent, and it is solved for transient state condition.
The model involves a single-phase flow, where oil flows through a rectangular domain
containing the media with porosity 0.9. In our case, the flow in the inlet and outlet sections is
turbulent and hence, standard k-epsilon with standard fall function model is chosen.
3.4.1.5 Porous condition
The flow through the porous media is considered to be laminar and is characterized by viscous
loss coefficients in the direction of flow that is y-direction. For this, Fluent’s porous media
model was enabled. The media is considered to be impermeable in the remaining two directions
i.e. x and z-direction, whose values of viscous resistance coefficients are four orders of
magnitude higher than in the y-direction. The viscous resistance coefficient and direction are
calculated from the experimental data that is available in the form of pressure against velocity
through the porous media which is determined from pressure drop test using Multipass method.
The pressure drop vs velocity is plotted to create a trendline, through these points an equation
is generated. The equation is now compared with the Darcy equation, from which the viscous
resistance coefficients are determined. Section 4.2 details the estimation of the viscous
resistance coefficients.
42
3.4.1.6 Oil Specifications
Fluid considered is standard Mobile DTE 25 from Exxon Mobil. It finds its application in many
hydraulics systems. Fluent library contains most of the standard fluids used for simulation. But
in our case, new fluid is created using the property of the oil which is listed in Table 3.7.
Type Mobil DTE 24
ISO VG30
Density,
Kg/m3 870
Viscosity, Cst 30
Table 3. 7: Oil Specification
3.4.1.7 Solver Setting
The phase coupled SIMPLE algorithm is used to couple the pressure and velocity equations in
our model. In this case, there is no particle or water injection. The second order upwind spatial
discretization method is chosen for momentum and turbulent equations in order to achieve a
fully converged solution of the flow field. The default values of under-relaxation factors are
chosen. The simulation is then initialized from the inlet and the model is run for a number of
time steps until a converged solution is obtained. The results are discussed in section 4.2 and
are compared with the experimental data.
The CFD model is simulated for 3 different flow rates, refer to Table 3.8
Parameters Simulation 1 Simulation 2 Simulation 3
Fluid Velocity, m/s 0.00295 0.00591 0.00886
Porosity 0.9 0.9 0.9
Fluid viscosity, Cst 30 30 30
Fluid density, kg/m3 870 870 870
Operating pressure, Pa 500000 500000 500000
Table 3. 8: Simulations
43
3.4.2 Case 2: Model with Fibers
3.4.2.1 Random fiber generation
The cellulose porous media is made of fibers that absorb water and retain it up to 10 to 100
times the weight of the water. Hydraulic oil with water passes through these fibers, where water
is absorbed and allowing the oil to flow through them. But in order to simulate water absorption
process, fibers have to be developed. These fibers can vary in length, diameter and also how
well they are packed together in a media. The porosity and permeability can also be varied and
the developed fibers can help us in determining the type of cellulose media for a different type
of water absorption applications. To reduce the complexity of the investigation, only X fibers
are created in the geometry model. However, the effective porosity of the modeled medium is
consistent with the real product.
Figure 3.17 shows a flow chart for the generation of these fibers. Firstly, a domain with length
(Dx), height (Dy) and thickness (Dz) is created with fibers start points and endpoints spread
along x, y, z directions respectively. Table 3.9 shows the domain dimensions based on media
size. Since, the fibers are randomly distributed, therefore, we use the rand () function in Excel
to create the start points 𝑥𝑖 , 𝑦𝑖, 𝑧𝑖 and endpoints 𝑥𝑗 , 𝑦𝑗 , 𝑧𝑗 of fibers. Table 3.10 shows the fiber
details. The endpoints are multiplied with the length of the fiber, which will help in creating
fibers of constant length. The number of fibers is generated based on the porosity required
which in our case is 0.9.
The number of fibers taken determines the porosity, which is calculated as shown below. The
number of fibers taken is 16 in order to attain 0.9 porosity.
Porosity = 𝑉𝑜𝑙𝑢𝑚𝑒 𝑜𝑓 𝑣𝑜𝑖𝑑 𝑠𝑝𝑎𝑐𝑒
𝑇𝑜𝑡𝑎𝑙 𝑣𝑜𝑙𝑢𝑚𝑒
Total Volume is the volume of the domain where the fibers are distributed.
Volume of void space= Volume of the domain (total volume)-Volume of number of fibers
44
Length of domain, Dx (media length) 29.64 mm
Height of domain, Dy (media height) 6.34 mm
Thickness of domain, Dz (media thickness) 2.6 mm
Volume of domain (Total Volume) 488.58 𝑚𝑚3
Table 3. 9: Domain details
Length of each fiber, Lf 15 mm
Diameter of each fiber, df 0.5 mm
Area of each fiber, Af 0.196 𝑚𝑚2
Volume of each fiber 2.94 𝑚𝑚3
Volume of 16 fiber 47.12 𝑚𝑚3
Table 3. 10: Fiber details
From the above table,
Volume of void space= 441.5 𝑚𝑚3
Therefore, Porosity = 441.5
488.58 =0.9
45
Figure 3. 17: Flowchart for generating 3D random fibers
3.4.2.2 Modeling Random fibers
Once the start points and end points are generated, the next step is to read the file .csv file and
develop the fibers in Ansys by assigning the diameter. The inlet zone is created with the exact
dimensions mentioned in section 3.4.1.1. The outlet zone is reduced in length to make the
46
computation faster. Hence, the new overall domain length is 8.717 mm. Figure 3.18 shows a
CFD model with random fiber distribution.
Figure 3. 18: Random fibers developed in the porous zone
47
3.4.2.3 Mesh Generation
The model with fibers are meshed using midside nodes (quadratic elements) as it provides a
better fit to geometry and it places an extra node on the middle of each side of each element
and projects these to surface. It is preferred because it captures the curvature in the solution
along with the element edges and across the element faces.
The element size of 0,4 mm is considered as the fiber diameter is 0,5 mm. Figure 3.19 shows
the mesh generated for the model. The quality of mesh plays an important role in the accuracy
and stability of the numerical computation. The orthogonal quality ranges from 0 to 1, where
0 is considered to be of low quality. The aspect ratio measures the stretching of the cell which
is maintained within the desired values. The skewness is defined as the difference between the
shape of the cell and the shape of the equilateral cell of equivalent volume. Highly skewed cells
can reduce the accuracy destabilize the problem. Also, due to the cylindrical curvatures of the
fiber, the curvature normal angle, which is the allowable angle that an element edge is allowed
to span for the fiber curvatures are set. Figure 3.20 shows the curvature normal angle around
the fiber and Table 3.11 shows the mesh quality for the model.
Orthogonal Quality
Max
Min
avg
1
0.002
0.5
Skewness
Max
Min
avg
0.99
0.001
0.49
Aspect ratio
Max
Min
avg
159
70
15
Curvature normal angle 40°
Table 3. 11: Mesh quality for the Model
48
Figure 3. 19: Mesh generated for fiber model
Figure 3. 20: Element edges with curvature normal angle.
3.4.2.4 Simulation Setup
In order to simulate water in oil flow, the DPM model is activated. The model is run for steady
state condition. But the particle or the droplet trajectories can be advanced in time in the
simulation for each iteration of the continuous phase. This is done by checking the Unsteady
particle tracking option in Fluent. Here, the particles will be advanced by the particle flow time
step.
49
The K-epsilon with standard wall functions is used for turbulence modeling. The porous model
is activated for the cells of the porous zone and porosity of 0.9 is set. The viscous resistance
coefficient with the correction factor is determined from the pressure drop vs velocity plot of
experimental data. The boundary condition remains the same for the model as mentioned in
section 3.4.1.3, but with an addition of fibers which is set as ‘Trap’ boundary condition for the
droplet to get trapped during the flow. Trapped water droplets depict the water absorbed by the
fibers. This trap condition is only available using Discrete phase model in fluent which makes
it distinct from various other models and thus estimating the number of water droplets
deposited on the fibers. Figure 3.22 shows the fibers which are set with ‘TRAP’ boundray
conditon.
Figure 3. 21: Fibers set with ‘TRAP’ Boundary condition
The volume of water in oil is very less, which is 0.01%. The droplets are injected from the inlet
surface of the model that releases particle stream from each facet of the surface. The mesh
model contains about 1360 mesh facet on the inlet surface. The droplets are made to inject
normal to the face of the surface. The number of droplets is usually injected as parcels. The
concept of parcels is that each parcel contains a number of droplets which makes computational
time, memory and cost of computation very less.
The initial parameters such as start time and end time, type of droplet, droplet velocity, droplet
diameter are also defined. These initial parameters provide the starting values for all the
dependent discrete phase variables that describe the instantaneous conditions of individual
droplets. Table 3.12 shows the simulations carried out for three different velocities for the
model.
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Continuous Phase – oil
Simulation 1 Simulation 2 Simulation 3
Oil velocity, m/s 0.0001773 0.000354 0.000709
Oil density, kg/m3 870 870 870
Oil viscosity, Cst 30 30 30
Operating pressure, Pa 500000 500000 500000
Discrete phase-water droplets
Velocity, m/s 0.0001773 0.000354 0.000709
Diamter of the droplet, mm 1e-5 1e-5 1e-5
Start of injection, s 0.2 0.2 0.2
End of injection, s 0.2 0.3 0.3
Density, kg/s 998 998 998
Total Flow rate. kg/s 0.000143 0.000143 0.000143
Table 3. 12: Simulations- Case 2 CFD model with fibers
3.5 Conclusion
The experiments were performed, and pressure drop measurements were recorded with the
least errors. The experiments were able to yield many factors that can be utilized in developing
the filter. But, it is limited to estimating the pressure drop and water content in oil. The tests
are carried out for three flow rates that yielded corresponding pressure drop values which
discussed in the next chapter.
The CFD model is developed considering the porous layers and its function. Each layer has its
importance, but only the layer which absorbs water is developed with fibers, other layers are
considered within the porous zone with a porosity of 0.9. Only X number of fiber were
generated, but the porosity is in consistent with the considered product. This is done in order
to make the simulation simple and faster. The CFD modelsare simulated with the same inputs
used in the experiments. The porous and DPM model in Ansys Fluent was successfully
implemented in determining the pressure drop and water content for the considered filter
element. The results are detailed in the next chapter.
51
4 Results and Discussions
4.1 Pressure drop for Flat sheet and pleated element from Multipass test
From the multipass test, the pressure drop for different flow rates for a flat sheet element and
the pleated element is obtained. This will give rise to a correction factor that can be directly
used in the CFD model. CFD model is designed without the pleats, the resistance to flow for a
pleated element is higher when compared to the flat sheet. Hence, the correction factor
determined from the experiments can give the exact viscous resistance coefficients that can be
used in the CFD simulations.
We know that as the temperature increases, the viscosity of the oil decreases. For reading to be
accurate, the temperature of the oil is maintained at 40°C throughout the experiment. This
results in good readings of pressure drop for different flow rates. The experiment is repeated 5
times, so the uncertainty is reduced, and the average value of the pressure drop is recorded.
Table 4.1 and 4.2 show the pressure drop values obtained for the Flat sheet and Pleated element.
From this, pressure drop (Pa) versus velocity (m3/s) is plotted which is shown in Figure 4.1.
Velocity in m/s Δp in Pa
2.955E-03 11000
5.910E-03 32000
8.865E-03 63000
Table 4. 1: Pressure drop for Flat sheet
Δp Velocity m/s
10500 1.77E-03
22000 3.55E-03
35000 5.32E-03
Table 4. 2: Pressure drop for Pleated Element
52
Figure 4. 1: Pressure drop vs Velocity for Flat and Pleated Element
From the above plot, the slope of the curves yields the correction factor. The viscous resistance
is different for flat sheet and pleated element. This correction factor is used in determining the
exact viscous resistance coefficient for a flat sheet. The resulting viscous resistance coefficient
is used in the case 2 CFD model for attaining a good validation with the experimental results.
Correction factor, CF = 𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝑃𝑙𝑒𝑎𝑡𝑒𝑑 𝐸𝑙𝑒𝑚𝑒𝑛𝑡
𝑆𝑙𝑜𝑝𝑒 𝑜𝑓 𝐹𝑙𝑎𝑡 𝑆ℎ𝑒𝑒𝑡
Correction Factor, CFD = 0.78
4.2 Flat sheet Analysis using CFD (CFD model without fibers)
The aim of the simulation work is to study the pressure drop occurring due to the porous
medium in the domain. Before the simulation is started, the viscous resistance coefficients must
be calculated from the pressure drop experiment for a flat sheet. From table 4.1, the pressure
drop against velocity through the porous component is extrapolated to determine the viscous
coefficients for the porous media.
The pressure drop vs velocity is plotted to create a trendline, through these points an equation
is generated. The equation is now compared with the Darcy equation, from which the viscous
resistance coefficients are determined.
0
10000
20000
30000
40000
50000
60000
70000
0 0,002 0,004 0,006 0,008 0,01
Dp
in
Pa
Velocity in m/s
Flat Sheet vs Pleated Element
Flat Sheet
Pleated Element
53
Figure 4. 2: Equation from the experimental result of Flat sheet
The plot from Figure 4.2, yields the following equation:
∆𝑝 = 6393342.86 𝑣
Where ∆𝑝 is the pressure drop in Pa and 𝑣 is the velocity in m/s
The above equation is compared with the Darcy equation as the flow is laminar through porous
media (Re<1).
∇𝑝 =𝜇
𝛼 𝑣
By comparing the above equations, the viscous resistance coefficient, 1
𝛼 is found to be to
8.19e+06 1
𝑚2 . The flow is through a 3D porous domain and is considered to be laminar,
therefore, it is characterized by viscous loss coefficients in the direction of flow which in the
present case is in the positive y-direction. The media is impermeable in the remaining two
directions i.e. x and z-direction, whose values of viscous resistance coefficients are four orders
of magnitude higher than in the y-direction. The table below gives the viscous resistance
coefficient in x, y, z directions.
∆𝑝= 6 393 342,86𝑣
0
10000
20000
30000
40000
50000
60000
70000
0 0,001 0,002 0,003 0,004 0,005 0,006 0,007 0,008 0,009 0,01
Dp
in P
a
Velocity m/s
Equation from experimental data
54
Direction
Vector Viscous resistance coefficient,
1
𝑚2
x 8.19e+10
y 8.19e+06
z 8.19e+10
Table 4. 3: Viscous resistance coefficients
Now, these values are utilized in case 1 CFD simulation, thus giving more accurate validation
for experimental and CFD results.
Figure 4.3, 4.4, 4.5 shows the contour plots for the pressure drop obtained from numerical
simulation of the flat sheet.
Figure 4. 3: Pressure drop when velocity is 0.00296 m/s
55
Figure 4. 4: : Pressure drop when velocity is 0.00591 m/s
Figure 4. 5: Pressure drop when velocity is 0.00887 m/s
Pressure drop in Pa Velocity in m/s
11486 2.955E-03
33112 5.910E-03
65171 8.865E-03
Table 4. 4: Pressure drop for Flat sheet from simulation
56
4.3 Experiment vs Numerical simulation of Flat sheet
From Table 4.1 and 4.4, it is seen that the values of pressure drop obtained from numerical
simulation lies within 5 % error margin of experimental pressure drop values. The results
obtained are very well in accordance with each other, the model forms a good basis for
developing the model further with 3D random fibers in the porous zone and simulate the water
absorption process. Figure 4.6 shows the pressure drop plot of experimental vs CFD results.
Figure 4. 6: Experimental vs CFD with 5% error for flat sheet
4.4 Pressure drop from the water absorption test
The water absorption test carried on the pleated filter element yielded the pressure drop which
is presented in Table 4.5. The experimental data is extrapolated to find the viscous resistance
coefficient.
Velocity in m/s Pressure drop in Pa
0.0001773 20000
0.000354 53000
0.000709 85000
Table 4. 5: Pressure drop from the water absorption test
0
10000
20000
30000
40000
50000
60000
70000
0 0,002 0,004 0,006 0,008 0,01
Dp
in P
a
Velocity in m/s
Exp vs CFD -Flat Sheet with 5 % error
Exp
CFD
57
Figure 4. 7: Pressure drop vs velocity from the experiment
The plot from Figure 4.7, yields the following equation,
∆𝑝 = 123408172.46 𝑣
The above equation is compared with the Darcy equation. The correction factor is also
incorporated in the viscous loss terms and we have the new viscous resistance coefficient with
a correction factor, refer Table 4.6.
Direction
Vector Viscous resistance coefficient,
1
𝑚2
x 1.44e+12
y 1.44e+08
z 1.44e+12
Table 4. 6: Viscous resistance coefficient
4.5 Pressure drop estimation using CFD model with fibers
The CFD model with fibers is solved for steady state condition. The values from table 4.6 are
utilized in CFD simulation. The oil is considered as continuous phase and water as discrete
phase. The volume of water in oil is 0.01% therefore, the water molecules are not causing a
∆𝑝= 1E+08 𝑣
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
0 0,0002 0,0004 0,0006 0,0008
Dp
in P
a
Velocity m/s
Equation from experimental data
58
huge difference in pressure drop values. Figure 4.8, 4.9 and 4.10 shows the contour plots for
the pressure drop obtained from the numerical simulation at velocity 0.0001773 m/s, 0.000354
m/s and 0.000709 m/s respectively.
Figure 4. 8: Pressure drop-Oil and water simulation for velocity of 0.0001773 m/s
Figure 4. 9:Pressure drop-Oil and water simulation for velocity of 0.0001773 m/s
Figure 4. 10: Pressure drop-Oil and water simulation for the velocity of 0.000709 m/s
59
Velocity in m/s Pressure drop in Pa
0.0001773 19500
0.000354 52500
0.000709 90000
Table 4. 7: Pressure drop from CFD simulation with fibers
4.6 Experiment vs Numerical simulation of model with fibers
From Table 4.5 and 4.7, it is seen that the values of pressure drop obtained from numerical
simulation lies within 5 % error margin of experimental pressure drop values. The results
obtained are very well in accordance with each other but increasing for higher velocities. This
indicates that the inertia forces are arising which are to be considered while simulating for high
velocity flows. Figure 4.6 shows the pressure drop plot of experimental vs CFD results.
Figure 4. 11: Experimental and CFD results
0
10000
20000
30000
40000
50000
60000
70000
80000
90000
100000
0 0,0002 0,0004 0,0006 0,0008
Dp
in P
a
Velocity m/s
Experimental vs CFD- with 5 % error
Experiment
CFD
60
4.7 Water removal efficiency
The experiment was added with 200 ml of water in 20- liters of the oil reservoir tank. The water
content was monitored at regular intervals of time. But in the present case, only the initial and
final water content values are considered. When the flow rates increase, the water retention
capacity of the filter element reduces. Filters are very efficient at low flow rates, as filter paper
is in a long time in contact with water droplets. But due to the limitation of the numerical
model, its compared with only single set of experimental values. The experimental and
simulation results are given in the table 4.8. The capacity and efficiency are calculated using
the formula,
Capacity C = 𝑾𝒇𝒆𝒅 − 𝑾𝒓𝒆𝒎𝒂𝒊𝒏𝒊𝒏𝒈
Efficiency % = 𝑾𝑪𝒂𝒑𝒕𝒖𝒓𝒆𝒅
𝑾𝒇𝒆𝒅 X 100 %
The amount of water droplet injected is equivalent to the number of mesh facet on the inlet
surface of the CFD model, which in our case is 1360. Ansys fluent injects 1360 particle streams
with total mass flow rate of 0.000143 kg/s that will follow the trajectory of the individual
particle/droplet. From the simulations, the fibers were able to trap 900 particle streams during
the flow which is equivalent to 0.159 kg of water deposited on the fibers. Table 4.8 shows the
capacity and efficiency of filter medium from experimental and numerical simulations. Figure
4.12 shows the mass concentration of water droplets on the fibers.
Methods Velocity
m/s
Water fed
𝑾𝒇𝒆𝒅
ml
Water
remaining
𝑾𝒓𝒆𝒎𝒂𝒊𝒏𝒊𝒏𝒈
ml
Water
captured
𝑾𝑪𝒂𝒑𝒕𝒖𝒓𝒆𝒅
ml
Capacity
C
ml
Efficiency
%
Experiment 0.0001773 200 20 180 180 90
CFD 0.0001773 200 40.1 159.85 159.85 80
Table 4. 8: Experimental and Simulation results of water absorption test
61
Figure 4. 12: Discrete phase concentration on the fibers
4.8 Limitation of the model
The CFD model with fiber only shows, the amount of water trapped and how the random fibers
are oriented. The fibers generated can take up any amount of water molecules without any
limit. But in actual cellulose porous media, these fibers have some limits in absorbing the water
and when they absorb water they tend to expand thereby reducing the pore size in the media.
This increases the pressure drop and after a certain point the filter element has to be changed.
The water retention property of the media also decreases when it has captured some of the
water molecules. Also, as the velocity increases the water absorbing ability of the cellulose
porous media reduces, this is because the water molecules has to be in contact with cellulose
media for a longer time. The longer the water molecules are in contact, the better the efficiency.
All these characteristics of a media are which the CFD model cannot include in its simulation.
But what the model can simulate is the stochastic collision-coalescence, breakup during the
flow and also its interaction with the continuous phase. The model can be further developed
for turbulent flows in porous domain by considering the inertial effects. The water properties
such as diameter, velocity can also changed based on requirements. Though there are
limitations, it can be further developed for studying the oil water separation process.
62
5 Conclusion
The preliminary objective was to carry out a pressure drop test across a porous medium using
a standard Multipass arrangement. The data from the test was fed into the model in order to
validate the data predicted by the computational model. The data considered during the
experiments were also used in the numerical model, therefore there is much consistency in the
results. The estimated pressure drop for flat sheets from simulations was compared with
experimental data and was found to be within 5% deviation from the experimental values. The
model thus formed a good base for further improvements and thereby introducing fibers into
the porous media.
In present work, a full-scale model of the pleated element was not developed, but a correction
factor based on the measurements of flat sheet vs pleated filter is used to extend the numerical
findings of flat sheet filter media to the pleated filter. The flat sheet model is now developed
with fibers in porous domain to simulate the water absorption process. The main aim was to
separate the water droplets from hydraulic oil flows using these generated fibers. These fibers
are randomly distributed in cellulose porous media. The 3D random fiber distribution in the
porous model was achieved using rand() function is excel, that created start and endpoints of
the fibers. The points were read into Ansys and thus an effective porous model consistent to
the real product was obtained. The goal for developing these fibers was to absorb and trap water
molecules which was successfully implemented by using the Discrete Phase model in Fluent.
The pressure drop and water removal efficiency was found to be in accordance with the
experimental data. Due to time constraints, water removal efficiency by the numerical model
is validated with only single set of experimental data and for steady state inflow conditions.
Therefore, there is a need for further simulations which can improve the model significantly.
The next section gives useful insights for carrying out further simulations which can be
included in investigation of water absorption process of the porous media.
63
6 Future work
The thesis developed just gives the overview and basic structure for simulating the water
absorption process. The model can be further developed by considering the following
recommendations for future studies.
• The numerical model does not include temperature effects in its simulation. At high
temperatures the viscosity changes and water molecules can evaporate, hence a user
defined function can be used to include these effects.
• In the present case, the water droplet is of constant diameter. But in actual hydraulic oil
flows, the droplet can be of different sizes. The variations in droplet diameters can be
achieved by using Rosin-Rammler distribution in Fluent.
• The numerical model can be included with Coalescence, Break up modelling in oil
flows. The droplets can coalesce or split into multiple droplets based on the impact
conditions. This physics model can be included in further developments of the model
but can be expensive due to increased computational time.
• The fibre distribution in the porous domain can be varied based on porosity. The fiber
diameter considered in the study is quite large, which can be reduced to make the model
realistic as possible. The smaller the diameter of fiber, the smaller should be the grid
size.
• The project involves two phase flows, where oil is considered to be continuous phase
and water as discrete phase. The hydraulic oil usually consists of solids, liquids and
gaseous contaminants. Further improvements can be made by introducing, three phase
or multiple phases in oil flows thereby predicting more accurate pressure drop and
particle interactions.
• The model is only for low Reynolds number where viscous forces are dominated.
Hence, there is further scope in including inertia forces to analyse and simulate the
model at high velocities.
• Generally, the permeability and resistance coefficients increase with time which is
common phenomena in filtration process. The model can include this effect by running
for transient inflow conditions.
64
7 References
Abetz, S. (2018, 08 09). Filtech. (K. Journal, Interviewer) From Kohan textile journal:
http://kohantextilejournal.com/filtech-largest-filtration-show-world-wide/
Costa, U. (1999). The role of inertia on fluid flow through disordered porous media. 420-424.
Darcy, H. (1856). Fontaines publiques de la ville de Dijon. Librairie des Corps Imperiaux
des Ponts et Chaussees et des Mines. Paris.
Deka, H., Biswas, G., Chakraborty, S., & Dalal, A. (2019). Coalescence dynamics of unequal
sized drops. Physics of fluid.
Fedorchenko, A., & Bang Wang, A. (2004). On some common features of drop impact on
liquid surfaces. Physics of Fluids 16, 1349-1365.
Fischer, K. (1935). New method for the dimensional analysis of the water content of liquids
and solid bodies. WILEY-VCH Verlag GmbH & Co.
Fluent, A. (2019). Ansys Fluent theory guide. From Ansys :
https://support.ansys.com/portal/site/AnsysCustomerPortal
Hai Ming Fu, Y. F. (2014, June). Experiment and Simulation on Pressure Drop of Pleated Air
Filters. Advanced Materials Research (Volume 960-961).
Haider, A., & Levenspiel, O. (1989). Drag coefficient and terminal velocity of spherical and
nonspherical particles. Power Technology, 63-70.
Hannifin, Parker. (2010, July 19). Filtration separation. Retrieved from Filtsep:
https://www.filtsep.com/filter%20media/features/hydraulic-fluids-controlling-
contamination-in/
ISO. (2008). Hydraulic fluid power -- Filters -- Multi-pass method for evaluating filtration
performance of a filter element.
Morsi, S., & Alexander, A. (2006). An investigation of particle trajectories in two-phase flow
systems. Journal of Fluid Mechanics, 193-208.
Parker Corporation. (2019, May 15). From parker.com: https://www.parker.com
Perm Inc. (2018, June 25). Fundamentals of Fluid Flow in Porous Media. From Perm Inc
TIPM Laboratory: http://perminc.com/resources/fundamentals-of-fluid-flow-in-
porous-media/chapter-1-introduction/
Prince, M., & Blanch, H. (1990). Bubble Coalescence and Break-Up in Air Sparged Bubble
Columns. AIChE Journal 36, 1485-1499.
Purchas, D., & Sutherland, K. (2011). Handbook of Filter media. Elsevier Advanced
Technology.
Skjetne, E., & Auriault, J. (1999). High-Velocity Laminar and Turbulent Flow in Porous
Media. Transport in Porous media, 131-147.
65
Tsuji, T. (2008). Multi-scale structure of clustering particles. World Conference of Particle
techology (WCPT5) (pp. 115-125). Orlando: Elsevier.
Versteeg, H., & Malalasekera, W. (2007). An introcution to Computational Fluid Dynamics:
The Finite Volume Method. Harlow: Pearson Education Limited.
Wright , J. (2008, January). Understanding Filter Efficiency and Beta Ratios. From
Machinery Lubrication: https://www.machinerylubrication.com
Yong, H., Park, C., Hu, Y., & Leal, L. (2001). The coalescence of two equal-sized drops in a
two-dimensional linear flow. Physics of Fluids, 1087-1106.
66
Appendix A:
General Settings used in Fluent for simulation: Case 1
Category Sub
category 1
Subcategory 2 Choice /Value Choice
/Value
GENERAL Solver Type
Velocity-
Formulation
Time
Gravity
Pressure based
Absolute
Transient
Gravitational
acceleration
x=0 m/𝑠2
y=0 m/𝑠2
z=0 m/𝑠2
OPERATING
CONDITIONS
Pressure Operating
Reference pressure
500000 Pa
x=0, y=0, z=0
MODEL Energy OFF
Viscous K-epsilon model
Near-wall
treatment
Model Constants
Standard
Standard wall functions
Default values for all
constants
Radiation OFF
MATERIAL Fluid Oil
Density
Viscosity
870 Kg/𝑚3
0.02784 Kg/ms
CELL ZONE Laminar Zone ON
Porous Zone ON
Viscous Resistance x= 8.19e+10 1/𝑚2
y= 8.19e+6 1/𝑚2
z=8.19e+10 1/𝑚2
Porosity 0.9
BOUNDARY
CONDITION
Inlet Velocity inlet Velocity magnitude
Turbulent Intensity
Hydraulic diameter
0.00295 m/s
5%
0.01547 m
Outlet Pressure outlet Gauge pressure 0 Pa
67
Backflow Turbulent
Intensity
5%
Backflow Hydraulic
diameter
0.01547 m
Internal Part Interior Default
Wall
Side Walls
Wall
Symmetry
Default
Default
SOLUTION
METHODS
Pressure-
Velocity
Coupling
Scheme SIMPLE
Spatial
Discretization
Gradient
Pressure
Momentum
Turb. Kinetic
energy
Turb. Diss. rate
Transient
Formulation
Least Square cell based
Second order
Second order upwind
Second order upwind
Second order upwind
First order implicit
Under
Relaxation
Factors
Pressure
Density
Body Force
Momentum
Turb. Kinetic
energy
Turb. Diss. Rate
Turbulent viscosity
0.3
1
1
0.7
0.8
0.4
1
Run
Calculation
Time Step Size (s)
Number of Time
Steps
Max Iteration/Time
Step
0.01
5000
30
Table A. 1: General settings in fluent for CFD model without fibers
68
Appendix B
General Settings used in Fluent for simulation: Case 2
Category Sub
category 1
Subcategory 2 Choice /Value Choice /Value
GENERAL Solver Type
Velocity-Formulation
Time
Gravity
Pressure based
Absolute
Steady
Gravitational
acceleration
x=0 m/𝑠2
y=0 m/𝑠2
z=0 m/𝑠2
OPERATING
CONDITIONS
Pressure Operating Reference
Pressure
500000 Pa
x=0, y=0, z=0
MODEL Energy OFF
Viscous K-epsilon model
Near-wall treatment
Model Constants
Standard
Standard wall functions
Default values for all
constants
Discrete Phase ON (See table B.1.1)
Radiation OFF
MATERIAL Fluid Oil
Density
Viscosity
870 Kg/𝑚3
0.02784 Kg/ms
Inert Particle Water Particle
Density
998 Kg/𝑚3
CELL ZONE Laminar Zone ON
Porous Zone ON
Viscous Resistance x= 1.44e+12 1/𝑚2
y= 1.44e+08 1/𝑚2
z=1.44e+12 1/𝑚2
Porosity 0.9
69
BOUNDARY
CONDITION
Inlet Velocity inlet Velocity magnitude
Turbulent Intensity
Hydraulic diameter
Discrete phase BC type
0.0001773 m/s
5%
0.01547 m
Reflect
Outlet Pressure outlet Gauge pressure
Backflow Turb. Intensity
Backflow Hydraulic
diameter
Discrete phase BC type
0 Pa
5%
0.01547 m
Escape
Internal Part Interior Default
Wall
Side Walls
Wall
Symmetry
Default
Default
Discrete phase BC type
Reflect
Fibers Wall Default
Discrete phase BC type
‘TRAP’
SOLUTION
METHODS
Pressure-
Velocity
Coupling
Scheme SIMPLE
Spatial
Discretization
Gradient
Pressure
Momentum
Turb. Kinetic energy
Turb. Diss. rate
Transient Formulation
Least-Square cell based
Second order
Second order upwind
Second order upwind
Second order upwind
First order implicit
Under
Relaxation
Factors
Pressure
Density
Body Force
Momentum
Turb. Kinetic energy
Turb. Diss. Rate
Turbulent viscosity
0.3
1
1
0.3
0.4
0.4
0.8
70
Run
Calculation
Number of Iteration 5000
Table B. 1: General settings in fluent for the CFD model with fibers
Category Sub
category 1
Sub category 2 Choice /Value
DISCRETE
PHASE
MODEL
Interaction Interaction with the continuous
phase
Update DPM sources very flow
iteration
Number of Continuous Phase
Iterations per DPM Iteration
ON
OFF
10
Particle Treatment Unsteady particle tracking
Particle time step
Number of time steps
ON
0.1
1
Tracking Parameters
Number of Maximum steps
Step Length Factor
9e+15
300
Numerics Tracking Options
Tracking scheme
Default values
Default values
Injections ON (See table B.1.2)
Table B.1. 1: Settings used in fluent for Discrete phase model
71
Category Sub category 1 Choice/ Value
INJECTION TYPE Surface
RELEASE FROM
SURFACE
Inlet
PARTICLE TYPE Inert
Material
Diameter distribution
Water liquid
Uniform
POINT PROPERTIES Diameter
Start time
End time
Velocity magnitude
Total flow rate
Inject from face normal direction
1e-05 m
0.2
0.3
0.0001773 m/s
0.000143 kg/s
ON
PHYSICAL MODEL Drag parameters Spherical drag law
Table B.1. 2: Settings for injection used in the DPM in fluent
Appendix C
The animated video of simple model of discrete phase getting trapped by the fibers is included
during the submission. File name’ Simple model demonstrating the DPM model’